Learn to estimate and find the volumes of rectangular prisms and triangular prisms.

Vocabulary volume

Volume is the number of cubic units needed to fill a space.

It takes 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism. There are 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes. Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.

Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. V = lwh Write the formula. V = 26 • 11 • 13 l = 26; w = 11; h = 13 V = 3,718 in3 Multiply.

Check It Out: Example 1 Find the volume of the rectangular prism. 16 in. 12 in. 29 in. V = lwh Write the formula. V = 29 • 12 • 16 l = 29; w = 12; h = 16 V = 5,568 in3 Multiply.

To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height.

Additional Example 2A: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. V = Bh Write the formula. V = ( • 3.9 • 1.3) • 4 1 2 __ B = • 3.9 • 1.3; h = 4. 1 2 __ V = 10.14 m3 Multiply.

The bases of a prism are always two congruent, parallel polygons. Caution!

Additional Example 2B: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = Bh Write the formula. V = ( • 6.5 • 7) • 6 1 2 __ B = • 6.5 • 7; h = 6. 1 2 __ V = 136.5 ft3 Multiply.

Check It Out: Example 2A Find the volume of each triangular prism. 7 m 1.6 m 4.2 m V = Bh Write the formula. V = ( • 4.2 • 1.6) • 7 1 2 __ B = • 4.2 • 1.6; h = 7. 1 2 __ V = 23.52 m3 Multiply.

Check It Out: Example 2B Find the volume of each triangular prism. 9 ft 5 ft 4.5 ft V = Bh Write the formula. V = ( • 4.5 • 9) • 5 1 2 __ B = • 4.5 • 9; h = 5. 1 2 __ V = 101.25 ft3 Multiply.

Understand the Problem Additional Example 3: Problem Solving Application Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes? 1 Understand the Problem The answer will be all possible dimensions for a case of 16 cubic boxes. List the important information: There are 16 tissue boxes in a case. The boxes are cubic, or square prisms.

Additional Example 3 Continued 2 Make a Plan You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes.

Additional Example 3 Continued Solve 3 You can make models using cubes to find the possible dimensions for a case of 16 cubes. The possible dimensions for a case of 16 cubic tissue boxes are the following: 16 x 1 x 1, 8 x 2 x 1, 4 x 4 x 1, and 4 x 2 x 2.

Additional Example 3 Continued 4 Look Back Notice that each dimension is a factor of 16. Also, the product of the dimensions (length • width • height) is 16, showing that the volume of each case is 16 cubes.

Understand the Problem Check It Out: Example 3 Suppose a paper company ships 12 cubic boxes of envelopes in each case. What are the possible dimensions for a case of envelope boxes? 1 Understand the Problem The answer will be all possible dimensions for a case of 12 cubic boxes. List the important information: There are 12 envelope boxes in a case. The boxes are cubic, or square prisms.

Check It Out: Example 3 Continued 2 Make a Plan You can make models using cubes to find the possible dimensions for a case of 12 boxes of envelopes.

Check It Out: Example 3 Continued Solve 3 You can make models using cubes to find the possible dimensions for a case of 12 cubes. The possible dimensions for a case of 12 cubic envelope boxes are the following: 12 x 1 x 1, 6 x 2 x 1, 4 x 3 x 1, and 3 x 2 x 2.

Check It Out: Example 3 Continued 4 Look Back Notice that each dimension is a factor of 12. Also, the product of the dimensions (length • width • height) is 12, showing that the volume of each case is 12 cubes.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 3. Find the volume of the figure shown. 3,600 cm3 153.3 cm3 38.13 cm3

Lesson Quiz for Student Response Systems 1. Identify the volume of a rectangular prism with length 25 cm, width 20 cm, and height 10 cm. A. 5,000 cm3 B. 5,225 cm3 C. 5,450 cm3 D. 5,650 cm3

Lesson Quiz for Student Response Systems 2. Identify the volume of a triangular prism with a height of 14 cm and a triangular base with base length 9.4 cm and height 4.5 cm. A. 326.4 cm3 B. 300.2 cm3 C. 296.1 cm3 D. 284.2 cm3

Lesson Quiz for Student Response Systems 3. Identify the volume of the figure shown. A. 72.52 cm3 B. 63.64 cm3 C. 62.5 cm3 D. 61.67 cm3